If one of the lines represented by ax^2 + 2hx | vedclass

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(C) The equation of the pair of lines is $ax^2 + 2hxy + by^2 = 0$. One of the lines bisects the angle between the positive coordinate axes,which is th

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$a+b = -2h$

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(C) The equation of the pair of lines is $ax^2 + 2hxy + by^2 = 0$. One of the lines bisects the angle between the positive coordinate axes,which is the line $y = x$ (slope $m = 1$). Since $y = x$ is a root of the homogeneous equation,we substitute $y = x$ into the equation: $ax^2 + 2hx(x) + bx^2 = 0$ $ax^2 + 2hx^2 + bx^2 = 0$ $(a + 2h + b)x^2 = 0$ For this to hold for all $x$,the coefficient must be zero: $a + 2h + b = 0$ Thus,$a + b = -2h$.

If one of the lines represented by $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the positive coordinate axes,then

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